Law_of_Exponents_Grade7 Final Presentation

Laws of exponent

1. Exponent RulesExponent Rules

2. PartsParts

When a number, variable, or expression is When a number, variable, or expression is
raised to a power, the number, variable, or raised to a power, the number, variable, or
expression is called the expression is called the basebase and the power is and the power is
called the called the exponentexponent..
n
b

3. What is an Exponent?What is an Exponent?

An exponent means that you multiply the base An exponent means that you multiply the base
by itself that many times.by itself that many times.

For example For example
xx
4 4
= = x x ● ● xx ●● xx ●● xx
22
6 6
= = 2 2 ● ● 22 ● ● 22 ● ● 22 ● ● 22 ● ● 22 = 64= 64

4. The Invisible ExponentThe Invisible Exponent

When an expression does not have a visible When an expression does not have a visible
exponent its exponent is understood to be 1.exponent its exponent is understood to be 1.
1
xx

5. Exponent Rule #1: Product RuleExponent Rule #1: Product Rule

When When multiplyingmultiplying two expressions with the two expressions with the
same base you same base you addadd their exponents. their exponents.

For exampleFor example

mn
bb
mn
b


42
xx 
42
x
6
x

2
22
21
22
21
2


3
2 8

6. Exponent Rule #1: Product RuleExponent Rule #1: Product Rule

Try it on your own:Try it on your own:

mn
bb
mn
b


73
.1 hh
33.2
2
1073
hh

312
33

27333 

7. Exponent Rule #2Exponent Rule #2

When When dividingdividing two expressions with the same two expressions with the same
base you base you subtractsubtract their exponents. their exponents.

For exampleFor example

m
n
b
b
mn
b


2
4
x
x

24
x
2
x

8. Exponent Rule #2Exponent Rule #2

m
n
b
b mn
b


2
6
.3
h
h

Try it on your own:Try it on your own:

3
3
.4
3

26
h
4
h

13
3 
2
39

9. Exponent Rule #3Exponent Rule #3

When raising a When raising a power to a powerpower to a power you you
multiplymultiply the exponents the exponents

For exampleFor example
mn
b)(
mn
b


42
)(x
42
x
8
x
22
)2(
22
2


4
2 16

10. Exponent Rule #3Exponent Rule #3

Try it on your ownTry it on your own
mn
b)(
mn
b


23
)(.5h
23
h
6
h
22
)3(.6
22
3


4
3 81

11. Exponent Rule #4Exponent Rule #4

When a product is raised to a power, each When a product is raised to a power, each
piece is raised to the powerpiece is raised to the power

For exampleFor example
m
ab)(
mm
ba
2
)(xy
22
yx
2
)52(
22
52 254 100

12. Exponent Rule #4Exponent Rule #4

Try it on your ownTry it on your own
m
ab)(
mm
ba
3
)(.7hk
33
kh
2
)32(.8
22
32 94 36

13. Exponent Rule #5Exponent Rule #5

When a quotient is raised to a power, both the When a quotient is raised to a power, both the
numerator and denominator are raised to the numerator and denominator are raised to the
powerpower

For exampleFor example






m
b
a
m
m
b
a









3
y
x
3
3
y
x

14. Exponent Rule #5Exponent Rule #5

Try it on your ownTry it on your own






m
b
a
m
m
b
a






2
.9
k
h
2
2
k
h






2
2
4
.10
2
2
2
4
4
16
 4

15. Zero ExponentZero Exponent

When anything, except 0, is raised to the zero When anything, except 0, is raised to the zero
power it is 1.power it is 1.

For exampleFor example

0
a1
( if a ≠ 0)

0
x1
( if x ≠ 0)

0
251

16. Zero ExponentZero Exponent

Try it on your ownTry it on your own

0
a1
( if a ≠ 0)

0
.11h1
( if h ≠ 0)

0
1000.12 1

0
0.13
undefined

17. Negative ExponentsNegative Exponents

If b If b ≠ 0, then≠ 0, then

For example For example

n
b
n
b
1

2
x
2
1
x

2
3
2
3
1
9
1


18. Negative ExponentsNegative Exponents

If b If b ≠ 0, then≠ 0, then

Try it on your own:Try it on your own:

n
b
n
b
1

3
.14h
3
1
h

3
2.15
3
2
1
8
1


19. Negative Exponents Negative Exponents

The negative exponent basically flips the part The negative exponent basically flips the part
with the negative exponent to the other half of with the negative exponent to the other half of
the fraction. the fraction.






2
1
b









1
2
b 2
b






2
2
x









1
2
2
x
2
2x

20. Math MannersMath Manners

For a problem to be completely For a problem to be completely
simplified there should not be any simplified there should not be any
negative exponentsnegative exponents

21. Mixed PracticeMixed Practice
9
5
3
6
.1
d
d
95
2

d
4
2

d
4
2
d

54
42.2 ee
54
8

e
9
8e

22. Mixed PracticeMixed Practice

5
4
.3q
54
q
20
q

5
2.4lp
555
2pl
55
32pl

23. Mixed PracticeMixed Practice
2
42
)(
)(
.5
xy
yx
22
48
yx
yx

2428 
 yx
26
yx
9
253
)(
.6
x
xx
9
28
)(
x
x

9
16
x
x

916
x
7
x

24. Mixed PracticeMixed Practice
6523246
)()(.7 pnmnm
301218812
pnmnm 
301281812
pnm


302030
pnm

25. Mixed PracticeMixed Practice
94
56
.9
da
da
9546 
 da
42
da
4
2
d
a
